the role of targeted predictors...
TRANSCRIPT
RUHRECONOMIC PAPERS
The Role of Targeted Predictors for
Nowcasting GDP with Bridge Models:
Application to the Euro Area
#559
Tobias KitlinskiPhilipp an de Meulen
Imprint
Ruhr Economic Papers
Published by
Ruhr-Universität Bochum (RUB), Department of EconomicsUniversitätsstr. 150, 44801 Bochum, Germany
Technische Universität Dortmund, Department of Economic and Social SciencesVogelpothsweg 87, 44227 Dortmund, Germany
Universität Duisburg-Essen, Department of EconomicsUniversitätsstr. 12, 45117 Essen, Germany
Rheinisch-Westfälisches Institut für Wirtschaftsforschung (RWI)Hohenzollernstr. 1-3, 45128 Essen, Germany
Editors
Prof. Dr. Thomas K. BauerRUB, Department of Economics, Empirical EconomicsPhone: +49 (0) 234/3 22 83 41, e-mail: [email protected]
Prof. Dr. Wolfgang LeiningerTechnische Universität Dortmund, Department of Economic and Social SciencesEconomics – MicroeconomicsPhone: +49 (0) 231/7 55-3297, e-mail: [email protected]
Prof. Dr. Volker ClausenUniversity of Duisburg-Essen, Department of EconomicsInternational EconomicsPhone: +49 (0) 201/1 83-3655, e-mail: [email protected]
Prof. Dr. Roland Döhrn, Prof. Dr. Manuel Frondel, Prof. Dr. Jochen KluveRWI, Phone: +49 (0) 201/81 49-213, e-mail: [email protected]
Editorial Offi ce
Sabine WeilerRWI, Phone: +49 (0) 201/81 49-213, e-mail: [email protected]
Ruhr Economic Papers #559
Responsible Editor: Roland Döhrn
All rights reserved. Bochum, Dortmund, Duisburg, Essen, Germany, 2015
ISSN 1864-4872 (online) – ISBN 978-3-86788-640-6The working papers published in the Series constitute work in progress circulated to stimulate discussion and critical comments. Views expressed represent exclusively the authors’ own opinions and do not necessarily refl ect those of the editors.
Ruhr Economic Papers #559
Tobias Kitlinski and Philipp an de Meulen
The Role of Targeted Predictors for
Nowcasting GDP with Bridge Models:
Application to the Euro Area
Bibliografi sche Informationen
der Deutschen Nationalbibliothek
Die Deutsche Bibliothek verzeichnet diese Publikation in der deutschen National-bibliografi e; detaillierte bibliografi sche Daten sind im Internet über: http://dnb.d-nb.de abrufb ar.
http://dx.doi.org/10.4419/86788640ISSN 1864-4872 (online)ISBN 978-3-86788-640-6
Tobias Kitlinski and Philipp an de Meulen1
The Role of Targeted Predictors for
Nowcasting GDP with Bridge Models:
Application to the Euro Area
Abstract
Using factor models, it has recently been shown that a pre-selection of indicators improves GDP forecasts in the very short-term. The aim of this paper is to adopt this research to the methodology of bridge models in combination with pooling approaches. Focusing on Euro Area GDP between 2005 and 2013, we fi nd that a selection of targeted predictors by means of soft- and hard-threshold algorithms improves the forecasting performance, especially during periods of economic crisis. While a critical number of indicators are needed to include all relevant information, adding additional indicators has a negative eff ect on forecasting performance, all the more, if the set of indicators becomes unbalanced.
JEL Classifi cation: C53, E37
Keywords: Forecasting; bridge equations; pooling of forecasts
May 2015
1 Both RWI. - We thank Roland Döhrn, Michael Roos, Christoph M. Schmidt and Torsten Schmidt for helpful comments and suggestions. - All correspondence to: Tobias Kitlinski, e-mail: [email protected]
1 Introduction
Reliable information on the current macroeconomic situation is an essential in-
gredient of decision making within private enterprises, central banks and govern-
ments. It helps to identify the current stage of the business cycle and thereby
builds an important starting point for assessing the future path of the economy.
Unfortunately GDP - which is the most important indicator of economic activity
- is released only quarterly and mostly with considerable delay.1 To estimate
GDP more timely, forecasters therefore refer to monthly economic indicators - of
which a plethora is available.
To condense the information contained in these indicators into a single fore-
cast, there are basically two strands of approaches. With the factor model (FM)
approach, the information is pooled before the regressions are estimated. The
numerous indicators are first combined in few common factors. Then, these fac-
tors jointly enter a regression equation to forecast GDP.2 The alternative strand
suggests to use indicators directly to produce different forecasts of GDP and to
condense the information contained in the forecasts in a second step, e.g. by
pooling techniques.
One approach in this field is Mixed-data sampling (MIDAS), which regresses
quarterly GDP on monthly indicator observations.3 Statistically less sophisti-
cated, Bridge models (BM) regress quarterly GDP on quarterly aggregates of
the monthly indicator values.4 Generating forecasts by means of simple linear
regressions, BM are a popular and widely used forecasting tool, which in general
1For the countries of the EU, the first official estimates are published six weeks after the endof the reference quarter.
2The literature on forecasting with FM is extensive, see (Diebold and Lopez, 1996; Giannoneet al., 2008). Applications to forecasting Euro Area GDP can be found in Angelini et al. (2011),Banbura and Runstler (2011), Marcellino et al. (2003) and Runstler et al. (2009).
3See e.g. Clements and Galvao (2008), Clements and Galvao (2009), Kuzin et al. (2011),Ferrara et al. (2014) and Foroni et al. (2015).
4Among the papers which put their focus on forecasting Euro Area GDP with BM areGrassmann and Keereman (2001), Diron (2008), Hahn and Skudelny (2008) and Drechsel andMaurin (2011).
4
do not perform worse than MIDAS and FM in terms of forecast precision.5
Despite their differences, all forecast approaches have one problem in common:
Which indicators should be taken into account in first place? In this regard,
forecasters face a trade-off: Focusing on only a few indicators bears the risk
of ignoring important information for forecasting, while considering too many
indicators may lead to increased error variance. Moreover, if a certain group
of predictors is overrepresented in the set of indicators, forecasts may be biased
since different indicator groups may explain different parts of GDP. This trade-
off generates the starting point of our paper, which poses the question, whether
reducing large indicator sets toward fewer carefully chosen predictors in a first
step can reduce forecast errors.
This question has recently become popular in the field of FM. Boivin and
Ng (2006) show that a smaller set of indicators can enhance forecast accuracy
if the influence of factors which provide high forecasting power declines with an
increasing panel size. Bai and Ng (2008) show that if the set of indicators is not
only small but restricted to those series which well explain the target variable,
this also improves forecasts of FM. In the present paper we analyze if this line of
reasoning can be adopted to the field of BM, which, to the best of our knowledge,
has not been done before.6
If we follow the arguments of Boivin and Ng (2006) and Bai and Ng (2008),
additional indicators (and thus additional forecasts) may harm forecast accuracy
if they only add noise. Whether this materializes in the field of BM is however
uncertain. Therefore, it is at the heart of our paper to investigate if a selection
of indicators provides a better forecasting performance of BM than including
5See Angelini et al. (2011), Kitchen and Monaco (2003), Schumacher and Dreger (2004),Antipa et al. (2012) and Schumacher (2014).
6This is at least true if we focus on forecasting with many low-dimensional bridge equations.Alternatively, it can be set up one single bridge equation including a small representative set ofindicators as regressors. In this strand, reducing the set of indicators is of course an importantaspect to prevent overfitting. However, since it can only be handled a limited number ofindicators, this strand is less suitable to investigate forecast accuracy with regard to the size ofthe indicator set.
5
all available information. On the one hand, like for FM, additional indicators
may trigger overrepresentation of a certain group of indicators and thus bias
forecasts of BM. On the other hand, adding as many indicators as possible to the
BM should not harm forecast precision: Additional indicators mean additional
forecasts and if these were useful in enhancing forecast accuracy, an appropriate
pooling technique would account for them, while if not, they would simply be left
out of consideration.
In focusing on the prediction of quarterly growth rates of Euro Area GDP
between 2005 and 2013, we apply two different data reduction rules, soft- and
hard-thresholding, to identify the so-called ”targeted predictors” from a large set
of predetermined indicators. To analyze the sensitivity of forecast accuracy with
regard to the set of targeted predictors, we test different thresholds. Constructing
quarterly aggregates of the respective targeted predictors, we set up bridge equa-
tions, run one-step-ahead forecasts and pool them by means of different weighting
schemes.
To mimic the ragged edge of the dataset a forecaster is faced with in real
time, we account for the monthly release pattern of our indicators. In a first step
we forecast the missing values by means of univariate autoregressive models. In
a second step we compute the quarterly aggregates. Since new indicator infor-
mation arrives every month, we run our forecasts monthly to correspond to the
monthly frequency of indicator releases. As GDP is released only quarterly, this
results in three successive forecast rounds on each quarterly GDP growth rate.
To not mix up the different levels of information, we conduct separate analyses
for forecasts made in the first, second and third forecasting round, respectively
It turns out that pre-selecting around 30 out of the 132 indicators provides
the lowest average forecast errors for most of the pooling approaches. While it
needs this critical number to include the relevant information for forecasting Euro
Area GDP, adding further indicators leads to overrepresentation of financial and
survey indicators - and apparently to lower forecast precision. Interestingly, the
forecasting performance of targeted predictors is significantly better in compari-
6
son to the whole indicator set if we leave out the period of the Great Recession.
The rest of the paper is structured as follows. Section 2 introduces the thresh-
old algorithms used for the pre-selection of indicators. Section 3 introduces the
system of bridge models and the different pooling techniques and it explains the
measurement of forecasting performance. Section 4 reports the empirical results
before section 5 concludes.
2 Selection of targeted predictors
Ideally, a set of predictors is chosen to include all relevant information for forceast-
ing the target variable. If, however, one predictor is highly correlated with an-
other, this bears the risk that instead of adding predictive power to the set, it
only adds noise, making forecasts less efficient. Further, if a certain group of pre-
dictors is overrepresented in the set of indicators, this may bias forecasts toward
the part of the target variable this group explains. Then a more parsimonious
but balanced set of predictors may provide more accurate forecasts.
Looking to the literature, the finding of Bai and Ng (2008) that identifying
a subset of suitable predictors is effective in improving forecast performance of
factor models was recently confirmed in several studies. Caggiano et al. (2011)
showed that using smaller subsets of the available large data set improves the
forecast performance of factor models for the six largest Euro Area economies,
the Euro Area aggregate and UK. Using Monte Carlo analyses, Alvarez et al.
(2012) show that small scale factor models outperform larger ones in terms of
forecast precision. To reduce the size of the data, they group indicator series into
different categories and choose one representative indicator from each group.
Focusing on forecasting models of Euro Area GDP, Girardi et al. (2014) ana-
lyzed dimension reduction methods. They used factor models that bridge factors
extracted from a large panel to quarterly national accounts and conclude that
using targeting predictors is an effective way to improve forecast performance. In
the field of BM, the related literature is scarce. To the best of our knowledge there
7
is only one paper, Bulligan et al. (2012), which investigates the effect of screening
targeted predictors on forecast precision. Focusing on Italian GDP, the authors
use different data reduction rules, namely hard- and soft-thresholding methods,
to reduce the dimension of the data and find that the forecasting performance
improves by screening targeted predictors. However, other than we do, Bulligan
et al. (2012) use the set of targeted predictors and extract the most informative
among them to set up a single forecast equation.
In the present paper, we adhere to the literature in using hard- and soft-
thresholding algorithms to select targeted predictors. The selection processes
start from a large set of 132 potentially relevant indicators, chosen in line with
the forecasting literature. It consists of real-economy indicators, survey indi-
cators, financial-market indicators, prices, as well as global economic indicators
(see Section A.2). All indicators enter the thresholding algorithms as stationary
variables. Below we describe how the algorithms work.
2.1 Hard-thresholding
Hard-thresholding algorithms aim to select those indicators which are most highly
correlated with the target according to some predetermined threshold. In order
to find those indicators, we adhere to Bair et al. (2006) and Bai and Ng (2008).
Precisely, for each of the 132 potentially relevant indicators we run a regression
of the quarterly growth rate of Euro Area GDP (yt) on an indicator-specific
function fi (xi,t−pi , (L)yt), where xi,t−pi is the potentially lagged indicator with
pi ∈ {0, ..., 6} and (L)yt is a lag polynomial of degree qi ∈ {0, ..., 4}. In each
regression, pi and qi are determined by the SIC to equal the optimal number of
lags. The estimation period consists of 24 quarters between 1999Q1 and 2004Q4.
In what follows, an indicator is selected as targeted predictor if and only if the
significance level (p-value) of the associated regression coefficient exceeds some
threshold α. In our forecast exercise we choose the common significance levels,
α = 0.9, α = 0.95 and α = 0.99.
While hard-thresholding is a very simple procedure, one obvious shortcom-
8
ing is that the selection process ignores the cross-correlations between indica-
tors. If the targeted predictors are highly correlated with each other, this bears
the risk that important information for forecasting is ignored. Methods of soft-
thresholding can remedy this deficiency.
2.2 Soft-thresholding
As soft-thresholding rule, we apply a forward selection algorithm, which will be
explained in the next paragraph. This algorithm explicitly accounts for the corre-
lations between indicators. Originally, soft-thresholding methods were applied in
biostatistics to find out if groups of genes in a DNA microarray can be applied to
predict the appearance of a certain disease (Donoho and Johnstone (1994)). Bai
and Ng (2008) used the soft-thresholding approach for the first time to determine
a smaller group of indicators from a large data set in the forecasting literature.
The forward selection algorithm proceeds stepwise. Within the estimation
period (1999Q1 − 2004Q4) it tries to find at each step the indicator which best
explains the part of the target not explained by the predictors selected so far.
Among our candidate set of 132 indicators, the algorithm starts from the
indicator (afterwards called x1) most highly correlated with y. Then, it searches
for a second indicator (x2 �= x1), which is most highly correlated with the residual
(u1) from the regression of y on x1, where x1 enters the regression with its optimal
lag p ∈ {0, ..., 6} according to the SIC. Regressing u1 on x2 again leaves some
unexplained part (u2) and again the algorithm searches among the remaining
indicators the one - then called x3 - that shows the highest correlation with u2.
The algorithm proceeds like this until there is no indicator left, where in each
regression of ui on xi+1, xi+1 enters with its optimal lag, restricted to a maximum
of six. As a result, we are provided with a ranking of indicators. To select the
targeted predictors, we simply select the k highest ranked indicators. In our
forecast exercise, we set k equal to the two extreme values 1 and 132 as well as
the multiples of 10 in between.
All in all, we end up with 17 different sets of targeted predictors, which
9
are related to 3 different thresholds with the hard-thresholding approach and 14
different thresholds with the soft-thresholding approach. Based on this variety, we
are given the opportunity to investigate the sensitivity of forecasting performance
with regards to the size and the contribution of the predictor set.
3 Forecast evaluation framework
Having selected different sets of targeted predictors, we compare them with regard
to their forecasting performance. The forecasts are derived from linear estima-
tions of Euro Area GDP on the predictors. To cope with the different frequencies
of GDP and indicators, we calculate quarterly aggregates of the monthly indi-
cators. In doing so, we only account for data which were available at the time
of each forecast and predict the respective missings with the help of univariate
autoregressive models.7 Since the ragged edge of the data frequently changes over
a month, we have to be precise in determining the date of each forecast.
For the present paper, we updated the data on July 10, 2014 and applied the
corresponding shape of the ragged edge to the whole forecast period.8 Figure 1
gives an illustration of this pattern for three successive months, in which one and
the same GDP growth rate is forecasted. As an example, it is considered the
monthly cycle of forecasting GDP in Q2. Since second-quarter GDP is released
around August 15, the three forecasting rounds take place on June 10, July 10
and August 10.
3.1 Bridge equations
For any set of targeted predictors and any forecasting round, we have 36 quarterly
GDP growth rates (y1 . . . y36) between 2005q1 and 2013q4 to be forecast one step
7For each indicator and each forecasting round, the number of lags of the autoregressivemodel is determined by the SIC and restricted to a maximum of 12 months.
8Using the data from mid-2014 rather than real-time data for each forecaast, it should benoted that our forecast exercise is pseudo-real time.
10
ahead. In the run-up of forecasting yt in round j, we determine a rolling window
of 24 in-sample quarters between t − 24 and t − 1 to estimate the relationship
between the targeted predictors and GDP growth.9
The in-sample estimations are based on a large variety of bridge equations
(system of bridge equations), which consists of three different subsystems. The
first subsystem includes K single indicator equations of the type
yτ = ck +
p∑m=0
βm,k · xk,τ−m + εk,τ τ = t− 24, . . . , t− 1 , (1)
where xk,· is the quarterly average of a representative predictor in the total set
of K targeted predictors. The second subsystem includes the K × K−12
possible
combinations of pairwise indicator equations of the type
yτ = ck,o+
p∑m=0
γm,k·xk,τ−m+
q∑n=0
γp+1+n,o·xo,τ−n+εk,o,τ τ = t−24, . . . , t−1 ; o �= k .
(2)
The third subsystem includes K equations each using one of the targeted predic-
tors as well as lagged dependent variables as regressors. A representative type of
such equation is given by
yτ = dk +
p∑m=0
δm,k · xk,τ−m +
q∑n=1
δp+n,k · yt−n + μk,τ τ = t− 24, . . . , t− 1 . (3)
In equations (1)-(3), parameters c and d denote the regression intercepts, the
β’s, γ’s and δ’s give the regression coefficients estimated by OLS, while ε and
μ denote usual zero-mean error terms. p and q give the number of lags of the
respective regressor, restricted to a maximum of 6 and optimized by the SIC. We
denote the optimal values of p and q by popt and qopt, respectively.
9Note that we need at least one forecast error if we want to pool forecasts based on theirpast performances. Hence, our investigation starts with the forecasts of GDP in 2005q2.
11
3.2 Forecasts
Based on estimates of β, γ, δ, c and d from equations (1)-(3), 2K+K×K−12
single
forecasts of yt are calculated in each forecasting round. Recall that in contrast to
the in-sample period, monthly indicator values are not entirely observable over
the forecast period. Hence, the quarterly aggregates x partly rely on forecasts of
monthly indicators, which in turn depend on the information available and thus
on the time it was computed. This is why the forecasting round j enters the
forecast equations below.
yjk,t = ck +
popt∑m=0
βm,k · xjk,t−m ∀ k = 1, . . . , K (4)
yjk,o,t = ck,o +
popt∑m=0
γm,k · xjk,t−m +
qopt∑n=0
γp+1+n,o · xjo,t−n ∀ k = 1, . . . , K (5)
yjk,y,t = dk +
popt∑m=0
δm,k · xjk,t−m +
qopt∑n=1
δp+n,k · yt−n ∀ k = 1, . . . , K , (6)
3.3 Pooling of forecasts
To end up with a single forecast in each forecasting round, we apply various
linear pooling approaches widely used in the literature: the mean, median, sev-
eral approaches that consider the in-sample fit (R2 and the AIC) as well as
approaches which weight models’ past forecasting performance (Trimming ap-
proaches).10 These approaches have in common that the pooled forecast is con-
structed as a weighted average of all or a subsample of underlying forecasts, where
individual weights sum to one.
We start with very simple approaches commonly used as benchmarks. The
most simple one is the mean forecast, which gives equal weight to all forecasts.
10In the literature it has been shown that forecast combination is able to reduce forecasterrors on average compared to single forecasts, see e.g. Stock and Watson (2003a), Stock andWatson (2004), Timmermann (2006) and Drechsel and Scheufele (2012a,b).
12
Another approach simply selects the median of all forecasts.
In a second group are pooling approaches that take into consideration the
in-sample fit of bridge equations. We use two approaches that assign weights
according to the variance of models’ in-sample estimation errors. We consider the
R2 and the AIC as information criteria, where the weights given to the forecasts
of the single model i = 1, . . . , 2K +K · K−12
are constructed in the following way:
ωICi,t = e−0.5·(|ICi,t−ICopt,t|)/
2K+K·K−12∑
h=1
e−0.5·(|ICh,t−ICopt,t|) . (7)
IC denotes the respective information criterium, R2 or AIC. Depending on the
criterium, ICopt,t either equals the largest R2 value (R2max,t) or the smallest AIC
value (AICmin,t) among the in-sample estimations.11
Using in-sample information for the assignment of weights is reasonable if the
estimated relationships remain stable over the forecast horizon. In the presence
of structural instabilities, however, models which perform good in-sample may
generate poor forecasts, see e.g. Stock and Watson (2003b). Taking this cri-
tique into consideration, we introduce a third group of pooling approaches, which
accounts for models’ past forecast errors. Since the forecast environment system-
atically changes over the forecasting rounds, we only account for past forecast
errors made in the same forecasting round to assign the weights.
A first approach, called trimming approach, takes the mean forecast from only
the best 1− x% of models in terms of past forecast performance (Timmermann,
2006).12 In line with the literature we set different thresholds of x, 0.25, 0.5
and 0.75. A second approach calculates weights according to the discounted
11Among the in-sample pooling approaches, note that we abstain from employing a ”restrictedleast squares estimator”. With the weights constructed from the estimated coefficients of re-gressing GDP on its single forecasts, the in-sample RMSFE would be minimized (Granger andRamanathan, 1984; Drechsel and Scheufele, 2012b). However, given our relatively small samplesize and 405 forecasts on each yt, the restricted least squares estimator is likely to suffer fromoverparameterization, as argued e.g. in Drechsel and Scheufele (2012b).
12Past forecast performance is measured in terms of the mean squared forecast error fromthe complete history of forecasts.
13
means of models’ past squared forecast errors. The weights assigned are inversely
proportional to the sum of discounted means of past squared forecast errors of
all models:13
ωji,t =
(∑t−1l=1 δ
t−l · (εji,l)2)−1
∑2K+K·K−12
h=1
(∑t−1l=1 δ
t−l · (εjh,l)2)−1 . (8)
3.4 Measuring Forecasting performance
With 8 different pooling approaches and three different forecasting rounds, there
are 3·8 levels to systematically compare the 17 different sets of targeted predictors
(3 sets for the hard- and 14 for the soft-threshold approach) with regard to their
forecast performance. To measure the forecast performance of the 3·8·17 forecastprocedures, we relate their RMSFE to the RMSFE conducted by a benchmark
autoregressive model of GDP growth
yt = a+
popt∑m=1
λm · yt−m , (9)
where each forecast yt is based on estimating a and the λm between t − 24 and
t − 1.14 With the forecasts of the benchmark AR model, the relative RMSFE
then reads as follows:
relative RMSFE =
√∑36t=1
(yt − yj,sw,t
)2√∑36
t=1 (yt − yt)2
. (10)
In equation (10), yj,sw,t describes the forecast of yt conducted in forecasting round j
which was pooled from the set of targeted predictors s using the pooling approach
w.
13In line with the literature, the discount factor δ is set equal to 0.95.14The number of lags popt ∈ {1, 2} is optimized in-sample by the SIC before each forecast.
14
While a relative RMSFE smaller than one means that the considered forecast
procedure outperforms the prediction accuracy of the benchmark AR model, we
need to consider the standard deviation of forecast errors to judge whether the
difference is statistically significant. In the literature, different tests on equal
predictive ability exist. One popular test goes back to Diebold and Mariano
(1995) which employs unconditional probability limits of coefficients’ estimates.
This is appropriate to compare the general predictive ability of two models.
However, to test which model performs better conditional on the date of the
forecast t, Giacomini and White (2006) have developed a conditional test of pre-
dictive ability, which uses parameter estimates βt instead. The null hypothesis is
tested using a Wald-type test statistic T . It states that the expected loss func-
tions L of the two compared forecast procedures are equal, where L increases
with the squared forecast error of the considered procedure.15 Following the lit-
erature, the Giacomini-White test should be given priority unless the uncertainty
concerning β does not bias forecast errors. In our analysis, the conditions of such
asymptotic irrelevance (West, 2006) are not fulfilled since coefficients as well as
estimation specifications may vary over time due to an updated rolling window
of in-sample quarters.16 Hence, we apply the Giacomini-White test to compare
our forecast procedures with the benchmark AR model.
4 Results
4.1 The sets of targeted predictors
In this section we briefly discuss the results of the indicator selection exercise.
The sets identified with the hard- and soft-thresholding algorithms can be found
in Tables 1−5. By construction, the soft-thresholding algorithm selects predictor
sets, which are very much balanced over the different groups. However, as the
15For a detailed description of the test and the test statistic see Giacomini and White (2006).16Moreover, using the Giacomini-White test, it allows us to compare the forecast accuracy
of nested and non-nested models.
15
whole indicator set is itself overrepresented by financial and survey indicators
for reasons of data availability, this unbalanced pattern emerges for some of the
thresholds. In fact, with k = 50 for the soft-thresholding approach, the vast
majority of real- and global-economic indicators are already included, while large
parts of financial and survey data is not.
Considering the hard-threshold approach, the results change. Since this ap-
proach ignores the correlation between indicators, the selected predictor sets are
less balanced: Relatively large weight is given to survey indicators while price
data are not covered at all. However, besides the sets of targeted predictors are
broadly balanced over the groups.
4.2 Forecasting performance
To compare the forecast ability of the 17 different sets of indicators, we conduct
the same forecast exercise for each set, as explained in section 3. The results
of these exercises are summarized by means of relative RMSFEs in tables 6−8,
where the three tables refer to forecasts conducted in the respective three different
forecasting rounds. Each Table is structured in the same way: The rows refer
to the pooling approaches, introduced in section 3.3. The columns refer to the
different sets of targeted predictors that enter the system of bridge equations.
Figures 2−7 provide a graphical analogue of Tables 6−8. Several interesting
patterns turn out.
First, the influence of the pooling approaches on forecast accuracy is much
less pronounced in the first compared to the second and third forecasting round.
This applies to both threshold approaches and is most conspicuous if we compare
the naive pooling approaches to out-of-sample schemes based on past forecasting
performance. Apparently, the more indicator data has to be predicted in first
place, the more biased becomes the assessment of bridge equations’ true forecast-
ing performance. Compared to Figures 2 to 6, the superiority of out-of-sample
schemes is much more pronounced than in Figures 3 to 7.
Second, the targeted predictors chosen by the hard-thresholding algorithm
16
generate smaller forecast errors if we compare sets with a similar number of
indicators. No matter the forecasting round and the pooling approach, choosing
20 targeted predictors by the soft-thresholding approach, this set performs worse
forecasts than the corresponding set of 20 targeted predictors chosen with the
hard-thresholding method (α = 0.05). This conclusion also stands if we compare
the best performing sets of both algorithms in each forecasting round and with
each pooling approach. We will turn to analyzing the backgrounds of this result
in more detail in the following paragraphs.
Third, the impact of the size of the indicator set shows an interesting pattern,
which emerges very similarly in all forecasting rounds, with all pooling approaches
and for both thresholding algorithms: While forecast accuracy increases with the
number of included predictors up to a certain quantity of around 20 indicators,
adding more indicators beyond this number does not improve the forecast accu-
racy. It even reduces it once the number of indicators becomes too large. This is
most apparent with the trimmed mean (75%) in the third forecasting round for
the soft-thresholding approach.
Forecast accuracy dramatically increases once we move from k = 10 to k = 20
and goes on increasing if we add another 10 indicators. However, taking more
than 30 indicators, the forecast performance gradually worsens. The set of k = 30
indicators includes the vast majority of real economic, global economic and price
indicators. Moving towards k = 132, the representation of financial market and
survey indicators becomes larger and so do forecast errors. As we will show in
the next paragraphs, this kind of overrepresentation leads to increased forecast
errors foremost during and after the Great Recession, 2008q2 − 2009q2.17 In
fact, our results are significant if we leave out the period of the Great Recession.18
17To define the period of the Great Recession we adhere to the Center for Economic andPolicy Research.
18The results of the Giacomini-White test reveal that there is no significant difference betweenthe relative RSMFEs of the pooled forecasts and the benchmark model. However, if we leaveout the Great Recession, our results become significant. This is mainly due to the high forecasterrors during this period.
17
In what follows, we want to go in more detail what is behind the impact of the
size (and composition) of the set of targeted predictors on forecast accuracy. To
simplify notation we denote by Sk and Hα the respective sets produced with soft-
and hard-thresholding, where the subscripts refer to the chosen thresholds. As a
first step, we identify the best-performing combination of pooling approach and
set of targeted predictors from each forecasting round and for both thresholding
algorithms separately. Throughout, the best pooling approach is given by the
trimmed mean (75%). Moreover, with soft-thresholding, S60, generates the lowest
relative RMSFE in the first forecasting round, while forecast errors are lowest
with S30 in the second and third round. Presumably, it needs less indicators
to cover the information for forecasting GDP as data availability improves over
the forecasting rounds. With hard-thresholding, it is always the same set (H0.05)
which generates the lowest errors in all forecasting rounds.19
Overall, it seems that a critical quantity of indicators is needed to cover the
relevant information for explaining GDP. Meanwhile, there is not much benefit
from adding further indicators. We conjecture that adding ”too” many variables
comes at the risk of increased error variance, and it comes at the risk of biased
forecasts if certain groups of indicators become overrepresented.
Based on the best-performing sets identified above, we want to go in further
detail and identify the quarters of the forecast periods, in which these sets show
their superiority. Again we proceed this analysis separately for each forecasting
round and for both thresholding algorithms, see Figures 8−13. In all six figures,
it is shown the time series of GDP growth as a solid line. Besides, it is shown
three series of forecast errors as bars. One refers to the errors conducted by
the respective best-performing set (blue bars). As benchmarks, the second one
refers to a set which comprises a very small number of indicators (S10 and H0.01
19While we focus on the typical significance levels, α = 0.9, α = 0.95 and α = 0.99 as arobustness check, we also calculated the forecasting errors in steps of 0.01 from α = 0.99 toα = 0.9 and it turned out that the results are very similar to those of the soft-thresholdingapproach. If a certain level of indicators is achieved, the forecasting performance does notimprove anymore.
18
respectively (black bars)) and the third one refers to the errors conducted with the
full set of indicators (red bars). For comparability reasons, all sets are combined
with the pooling approach trimmed mean (75%).20
Comparing the three sets with regard to their forecast performances in each
figure, a clear pattern emerges. While the differences are not much pronounced in
”calm times” of stable growth, they became apparent during the Great Recession
and the European Debt Crises. Precisely, we can identify the quarters between
2008Q4 − 2009Q2 and between 2011Q3 − 2012Q3 as periods, where the best-
performing sets stand out.
Hence, we pick two characteristic quarters, 2009Q1 and 2012Q3, to illustrate
which bridge equations and thus predictors help to create the superiority of the
best-performing sets. Again we compare them to S10 and H0.01 as well as to
the full set S132 = H1. For simplicity, we only focus on the third forecasting
round (Figure 12 and Figure 13 ), in which forecasts are least affected by missing
indicator data and we apply the trimmed mean (75%) as the pooling approach.
Starting with 2009Q1, where GDP collapsed by −2.9% qoq, all sets produced
too positive pooled forecasts. While the deviation is relatively small with the
respective best sets (0.31 percenatage points (pp) with H0.05 and 0.55 pp with
S30), the small sets S10 and H0.01 produce errors of 0.95 pp and 1.45 pp. Taking
a look inside the indicator sets, the small sets lack most of the financial variables,
which proved to be very important predictors during the Great Recession. Above
that, H0.01 also discards all real economic data, which well explained GDP at that
time, particularly in combination with financial indicators. In addition, the small
set includes only one survey indicator, while the optimal sets takes five survey
indicators into account.
Turning to the full set, the error amounted to 0.96 pp in 2009Q1. While this is
very much the same as the one conducted by H0.01, the background is completely
20In all forecasting rounds and in combination with both thresholding approaches, thetrimmed mean (75%) showed the lowest relative RMSFE. However, we cannot determine anysignificant difference between the trimmed mean (75%) and the other applied threshold ap-proaches.
19
different. Rather than a lack of variables, it suffers from too many indicators.
Since half of the indicators of the full set are related to survey data, the forecasts
became biased. There is no clear pattern which of the survey indicators works
poorly, but if the share of survey indicators becomes too large, this worsens the
forecasting performance.
Turning to the forecasts for 2012Q3, the explanation is different. The general
deviation is smaller since the decline of GDP was not quite as pronounced as in
2009q1. Nevertheless, the best performing sets (S30 and H0.05) outperformed S10
and H0.01 as well as the full set S132 = H1. This is mainly due to the different
number of survey indicators included in the indicator sets. At least a certain
number of them perform well during the European Debt Crises. This result is
not surprising since the weak economic activity originated from uncertainty in
the Euro area.21
The small sets S10 and H0.01 lack most of the survey indicators. Hence, their
deviation (S10 with −0.53 pp and H0.01 with −0.62 pp) is higher than for the best
performing models (0.06 pp with H0.05 and 0.12 pp with S30). The reason for the
weak forecasting performance of the full sets is mainly the same as for 2009q1.
However, this time too many of the real economic indicators (among others) are
included which perform poorly.
5 Conclusions
Short-term forecasting relies on timely available indicators with a higher fre-
quency than the target variable. In recent times, the availability of indicators
has grown and the question arises if a selection of indicators provides a better
forecasting performance than including all available information. In this paper we
apply two threshold algorithms in combination with various pooling approaches
to analyze if different sizes of indicator sets have an impact on the forecasting
21For example, the Policy Uncertainty Index for the Euro Area shows several peaks in 2012and indicates high uncertainty (Baker et al., 2013).
20
performance of bridge models to forecast Euro Area GDP. Furthermore, we focus
on the performance of the different sizes of indicator sets during periods of weak
economic activity.
It turns out that a selection of indicators improves the forecasting performance
in comparison to a benchmark model, especially in times of weak economic ac-
tivity. This is true if forecasts for Euro Area GDP are conducted with predicted
values for the respective missings of the indicators. However, the more official
data is published the more important becomes a selection of indicators. More
precisely, the combination of the hard-thresholding algorithm and the trimmed
mean (75%) shows always the lowest relative RMSFE in relation to the benchmark
model. Nevertheless, these results are only statistically significant if the Great
Recession is not included. By highlighting the important role of carefully select-
ing predictors especially in turbulent times of large turning points, we believe to
substantially contribute to the existing literature on short-term forecasting.
21
References
Alvarez, R., Camacho, M., and Perez-Quiros, G. (2012). Finite sample performance
of small versus large scale dynamic factor models. CEPR Discussion Papers 8867,
C.E.P.R. Discussion Papers.
Angelini, E., Mendez, G. C., Giannone, D., Reichlin, L., and Runstler, G. (2011).
Short-term forecasts of euro area GDP growth. Econometrics Journal, 14(1):25–44.
Antipa, P., Barhoumi, K., Brunhes-Lesage, V., and Darne, O. (2012). Nowcasting
German GDP: A comparison of bridge and factor models. Journal of Policy Modeling,
34(6):864–878.
Bai, J. and Ng, S. (2008). Forecasting economic time series using targeted predictors.
Journal of Econometrics, 146(2):304 – 317. Honoring the research contributions of
Charles R. Nelson.
Bair, E., Hastie, T., Paul, D., and Tibshirani, R. (2006). Prediction by supervised
principal components. Journal of the American Statistical Association, 101(473).
Baker, S. R., Bloom, N., and Davis, S. J. (2013). Measuring Economic Policy Uncer-
tainty. Technical Report 13-02, Chicago Booth Research Paper.
Banbura, M. and Runstler, G. (2011). A look into the factor model black box: Pub-
lication lags and the role of hard and soft data in forecasting GDP. International
Journal of Forecasting, 27(2):333–346.
Boivin, J. and Ng, S. (2006). Are more data always better for factor analysis? Journal
of Econometrics, 132(1):169–194.
Bulligan, G., Marcellino, M., and Venditti, F. (2012). Forecasting economic activity
with higher frequency targeted predictors. Temi di discussione (Economic working
papers) 847, Bank of Italy, Economic Research and International Relations Area.
Caggiano, G., Kapetanios, G., and Labhard, V. (2011). Are more data always better
for factor analysis? Results for the euro area, the six largest euro area countries and
the UK. Journal of Forecasting, 30(8):736–752.
22
Clements, M. P. and Galvao, A. B. (2008). Macroeconomic forecasting with mixed-
frequency data: Forecasting output growth in the United States. Journal of Business
& Economic Statistics, 26(4):546–554.
Clements, M. P. and Galvao, A. B. (2009). Forecasting US output growth using leading
indicators: an appraisal using MIDAS models. Journal of Applied Econometrics,
24(7):1187–1206.
Diebold, F. X. and Lopez, J. A. (1996). Forecast Evaluation and Combination. In
Handbool of Statistics, pages 241–268. North-Holland.
Diebold, F. X. and Mariano, R. S. (1995). Comparing Predictive Accuracy. Journal of
Business & Economic Statistics, 13(3):253–63.
Diron, M. (2008). Short-term forecasts of euro area real GDP growth: an assessment of
real-time performance based on vintage data. Journal of Forecasting, 27(5):371–390.
Donoho, D. L. and Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrink-
age. Biometrika, 81:425–455.
Drechsel, K. and Maurin, L. (2011). Flow of conjunctural information and forecast of
euro area economic activity. Journal of Forecasting, 30(3):336–354.
Drechsel, K. and Scheufele, R. (2012a). The Financial Crisis from a Forecaster’s Per-
spective. Kredit und Kapital, 5(1):1–28.
Drechsel, K. and Scheufele, R. (2012b). The performance of short-term forecasts of the
German economy before and during the 2008/2009 recession. International Journal
of Forecasting, 28(2):428 – 445.
Ferrara, L., Marsilli, C., and Ortega, J.-P. (2014). Forecasting growth during the
Great Recession: is financial volatility the missing ingredient? Economic Modelling,
36:44–50.
Foroni, C., Marcellino, M., and Schumacher, C. (2015). Unrestricted mixed data sam-
pling (MIDAS): MIDAS regressions with unrestricted lag polynomials. Journal of
the Royal Statistical Society: Series A (Statistics in Society), 178(1):57–82.
23
Giacomini, R. and White, H. (2006). Tests of Conditional Predictive Ability. Econo-
metrica, 74(6):1545–1578.
Giannone, D., Reichlin, L., and Small, D. (2008). Nowcasting: The real-time informa-
tional content of macroeconomic data. Journal of Monetary Economics, 55(4):665–
676.
Girardi, A., Golinelli, R., and Pappalardo (2014). The Role of Indicator Selection in
Nowcasting Euro Area GDP in Pseudo Real Time. Working Papers wp919, Dipar-
timento Scienze Economiche, Universita’ di Bologna.
Granger, C. W. and Ramanathan, R. (1984). Improved methods of combining fore-
casting. Journal of Forecasting, 3(2):197–204.
Grassmann, P. and Keereman, F. (2001). An indicator-based short-term forecast for
quarterly GDP in the euro area. European Economy - Economic Papers 154, Direc-
torate General Economic and Monetary Affairs (DG ECFIN), European Commission.
Hahn, E. and Skudelny, F. (2008). Early estimates of euro area real GDP growth: a
bottom up approach from the production side. Working Paper Series 0975, European
Central Bank.
Kitchen, J. and Monaco, R. (2003). Real-Time Forecasting in Practice: The U.S.
Treasury Staff’s Real-Time GDP Forecast System. Business Economics, 38(4):10–
19.
Kuzin, V., Marcellino, M., and Schumacher, C. (2011). MIDAS vs. mixed-frequency
VAR: Nowcasting GDP in the euro area. International Journal of Forecasting,
27(2):529 – 542.
Marcellino, M., Stock, J. H., and Watson, M. W. (2003). Macroeconomic forecasting in
the Euro area: Country specific versus area-wide information. European Economic
Review, 47(1):1–18.
Runstler, G., Barhoumi, K., Benk, S., Cristadoro, R., Reijer, A. D., Jakaitiene, A.,
Jelonek, P., Rua, A., Ruth, K., and Nieuwenhuyze, C. V. (2009). Short-term fore-
24
casting of GDP using large datasets: a pseudo real-time forecast evaluation exercise.
Journal of Forecasting, 28(7):595–611.
Schumacher, C. (2014). MIDAS and bridge equations. Discussion Papers 26/2014,
Deutsche Bundesbank, Research Centre.
Schumacher, C. and Dreger, C. (2004). Estimating Large-Scale Factor Models for
Economic Activity in Germany: Do They Outperform Simpler Models? Journal
of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik),
224(6):731–750.
Stock, J. H. and Watson, M. M. (2003a). How did leading indicator forecasts perform
during the 2001 recession? Economic Quarterly, (Sum):71–90.
Stock, J. H. and Watson, M. W. (2003b). Forecasting Output and Inflation: The Role
of Asset Prices. Journal of Economic Literature, 41(3):788–829.
Stock, J. H. and Watson, M. W. (2004). Combination forecasts of output growth in a
seven-country data set. Journal of Forecasting, 23(6):405–430.
Timmermann, A. (2006). Forecast Combinations, volume 1 of Handbook of Economic
Forecasting, chapter 4, pages 135–196. Elsevier.
West, K. D. (2006). Forecast Evaluation, volume 1 of Handbook of Economic Forecast-
ing, chapter 3, pages 99–134. Elsevier.
25
A Appendix
A.1 Tables and Graphs
A.2 Selection of targeted predictors
Table 1: Selection of Real Economic indicators
Hard Softthreshold α threshold k
0.01 0.05 0.1 1 10 20 30 40 50 60 70 80 90 100 110 120 132
Prod.; Total industry excl. constr.1 x x x x x x x x x x x x x
Prod.; Mining & quarrying1 x x x x x x x x x x x x
Prod.; Durable consumer goods1 x x x x x x x x x x x x x x
Prod.; Non-durable consumer goods1 x x x x x x x x x x x x x
Prod.; Energy1 x x x x x x x x x
Prod.; Capital goods1 x x x x x x x x x x x x
Prod.; Intermediate goods1 x x x x x
Prod.; Manufacturing1 x x x x x x x x x x
Prod.; Electricity, gas, steam etc.1 x x x x x x x x x x x x x
Prod.; Construction1 x x x x x x x x x x x x x
Retail sales; Volume1 x x x x x x x x x x x x x
Registrations; New passenger cars;2 x x x x x x x x x
Earnings, per hour1 x x x x x x x x x x x1 = EMU; 2005=100, sa;2 = EMU; 1000;
26
Tab
le2:
Selection
ofSurvey
indicators
Hard
Soft
thre
shold
αth
resh
old
k0.01
0.05
0.1
110
20
30
40
50
60
70
80
90
100
110
120
132
EM
UBusiness
confidence;M
anufactu
ring;%,sa
xx
EM
UBusiness
climate
;M
anufactu
ring;2000=100,sa
xx
xEM
UOrd
erbook
levelassessment;
Manufactu
ring;%,sa
xEM
USto
cksassessment(fi
nished
pro
ducts);
Manufactu
ring;%,sa
xx
xx
xEM
UEmploymentexpecta
tionsforth
emonth
sahead;M
anufactu
ring;%,sa
xx
xx
xx
xEM
UPro
duction
trend
obse
rved
inre
centmonth
s;M
anufactu
ring;%,sa
xx
xx
xEM
UExport
ord
erbook
levelassessment;
Manufactu
ring;%,sa
;x
xx
EM
UPro
duction
expecta
tionsforth
emonth
sahead;M
anufactu
ring;%,sa
xx
xx
xx
xx
xEM
USellin
gpriceexpecta
tionsforth
emonth
sahead;M
anufactu
ring;%,sa
xx
xx
xx
xx
EM
UAss.ofexport
ord
erbook;M
anufactu
reofmachin
ery
and
equip
ment;
%,sa
xx
EM
UAss.ofexport
ord
erbook;M
anufactu
reofmoto
rvehiclesetc
.,%,sa
xx
xx
xx
xEM
UAss.oford
erbook;M
anufactu
reofmachin
ery
and
equip
ment;
%,sa
xx
xEM
UAss.oford
erbook;M
anufactu
reofmoto
rvehiclesetc
,%,sa
xx
xx
xx
xEM
UAss.oford
erbook;Oth
ermanufactu
ring;%,sa
xx
xx
EM
UAss.ofstocks(fi
n.pro
d.);M
anufactu
reofelectricalequip
ment;
%,sa
xx
xx
xEM
UAss.ofstocks(fi
n.pro
d.);M
anufactu
reofmachin
ery
and
equip
ment;
%,sa
xx
xx
xx
xx
xx
xEM
UAss.ofstocks(fi
n.pro
d.);M
anufactu
reofmoto
rvehiclesetc
.,%,sa
xx
xx
xx
xx
xx
xx
EM
UAss.oford
erbook;M
anufactu
reofelectricalequip
ment;
%,sa
xx
xx
xx
xEM
UAsse.ofexport
ord
erbook;M
anufactu
reofelectricalequip
ment;
%,sa
xx
xx
xx
xEM
UIn
d.ConfidenceIn
dicato
r;M
anufactu
reofelectricalequip
ment;
%,sa
xx
xEM
UIn
d.ConfidenceIn
dicato
r;M
anufactu
reofmachin
ery
and
equip
ment;
%,sa
xx
xx
xEM
UIn
d.ConfidenceIn
dicato
r;M
anufactu
reofmoto
rvehiclesetc
.,%,sa
xx
xx
xx
xx
xx
xEM
USto
cksassessment(fi
nished
pro
ducts);
Manufactu
ring;%,sa
xx
xx
xEM
UBusiness
confidence;Constru
ction
industry
;%,sa
xx
xx
xEM
UActivity
trend
obse
rved;Civil
engin
eering;%,sa
xx
xx
xx
xx
xEM
UPriceexpecta
tions;
Constru
ction
industry
;%,sa
xx
xx
xx
EM
UEmploymentexpecta
tions;
Constru
ction
industry
;%,sa
xx
xx
xx
EM
UOrd
erbook
levelassessment;
Constru
ction
industry
;%,sa
xx
xx
xx
xx
EM
UActivity
trend;Constru
ction
industry
;%,sa
xx
xx
EM
UBusiness
confidence;Reta
iltrade;%,sa
xx
xx
xx
EM
UBusiness
expecta
tionsovernext3
month
s;Reta
iltrade;%,sa
xx
xx
xx
xx
xx
EM
UBusiness
activity
(sales)
overpast
3month
s;Reta
iltrade;%,sa
xx
xx
xx
xx
xEM
UEmploymentexpecta
tionsovernext3
month
s;Reta
iltrade;%,sa
xx
xx
xx
xx
xx
xEM
UOrd
ering
inte
ntionsovernext3
month
s;Reta
iltrade;%,sa
xx
xx
xx
xx
xEM
UDemand
developmentoverpast
3month
s;Serv
ices;
%,sa
xx
xx
xx
xx
xx
xx
xx
xx
EM
UDemand
expecta
tionsovernext3
month
s;Serv
ices;
%x
xx
xx
xx
xx
EM
UEmploymentexpecta
tionsovernext3
month
s;Serv
ices;
%,sa
xx
xx
xx
EM
UEmploymentdevelopmentoverpast
3month
s;Serv
ices;
%,sa
xx
xx
xx
xx
xEM
UBusiness
confidence;Serv
ices;
%,sa
xx
xx
xx
xEM
UBusiness
situ
ation
developmentoverpast
3month
s;Serv
ices;
%,sa
xx
xx
xx
xx
xx
EM
UEconomic
sentiment;
Business
secto
r&
consu
mers;sa
xx
xx
xEM
ULeadin
gin
dicato
r(O
ECD);
Amplitu
deadju
sted,long
term
avera
ge=
100
xx
xx
xx
xx
xEM
UConsu
merconfidence;%,sa
xEM
UConsu
merclimate
(OECD);
Norm
al=
100,sa
xEM
UConsu
merclimate
;2000=100,sa
xEM
UM
ajorpurchase
splanned,next12
month
s;Consu
mers;%,sa
xx
xx
xx
xx
xx
EM
UM
ajorpurchase
sinte
nded,currently;Consu
mers;%,sa
xx
xx
xEM
USavin
gsplanned,next12
month
s;Consu
mers;%,sa
xx
EM
USavin
gsinte
nded,currently;Consu
mers;%,sa
xx
xEM
UUnemploymentexpecta
tions,
next12
month
s;Consu
mers;%,sa
xx
xx
xx
EM
UFin
ancialsitu
ation,last
12
month
s;Consu
mers;%,sa
xx
xx
EM
UFin
ancialsitu
ation,next12
month
s;Consu
mers;%,sa
xx
xx
xx
EM
UGenera
leconomic
situ
ation,last
12
month
s;Consu
mers;%,sa
xEM
UGenera
leconomic
situ
ation,next12
month
s;Consu
mers;%,sa
xx
xx
xx
xx
xx
EM
UPricetrend
assessment,
last
12
month
s;Consu
mers;%,sa
xx
xx
xx
xx
EM
UPricetrend
expecta
tions,
next12
month
s;Consu
mers;%,sa
xx
xx
xx
xx
EM
USta
tementon
financialsitu
ation
ofhouse
hold
;Consu
mers;%,sa
xx
xx
xx
EM
UUnemploymentra
te;Base
don
surv
ey
data
;%
oflaborforc
e,sa
xx
xx
xx
x
27
Tab
le3:
Selection
ofPrice
indicators
Hard
Soft
thre
shold
αth
resh
old
k0.01
0.05
0.1
110
20
30
40
50
60
70
80
90
100
110
120
132
EM
UPro
ducerprice;Excl.
energ
y;2005=100
xx
xx
xx
xx
xx
xx
xEM
UPro
ducerprice;2005=100
xx
xx
xx
xx
xx
xEM
UConsu
merprice;Harm
onized
toEU
guid
elines;
2005=100,sa
xx
xx
xx
xx
xx
xx
xEM
UConsu
merprice;Energ
y,harm
onized
toEU
guid
elines;
2005=100
xx
xEM
UConsu
merprice;In
dustrialgoods,
harm
onized
toEU
guid
elines;
2005=100
xx
xx
xx
xx
xx
xEM
UExport
price;2005=100
xx
xx
xx
xx
xx
EM
UIm
port
price;2005=100
xx
x
28
Tab
le4:
Selection
ofFinan
cial
marketindicators
Hard
Soft
thre
shold
αth
resh
old
k0.01
0.05
0.1
110
20
30
40
50
60
70
80
90
100
110
120
132
EM
UM
SCIsh
are
pricein
dex;Euro
base
d,1996.12.31=100
xx
xx
xx
xx
xx
xx
EM
UAssets
ofM
FIs;Loansto
Euro
are
apr.
secto
r;Outsta
ndin
gamount,
bn
Euro
xx
xx
xx
xx
xx
xx
EM
UAssets
ofM
FIs;Loansto
Euro
are
aNon-M
FIs;Outsta
ndin
gamount,
bn
Euro
xx
xx
xx
xx
xx
EM
UM
oney
supply
M1;Level,
bn
Euro
,sa
xx
xx
xx
xx
xx
xEM
UM
oney
supply
M2;Level,
bn
Euro
,sa
xx
xx
xx
xx
xx
xx
xx
xx
EM
UM
oney
supply
M3;Level,
bn
Euro
,sa
xx
xx
xx
xx
xx
xx
xEM
UCre
dit;Loansto
Euro
are
aprivate
secto
r;Level,
bn
Euro
xx
xx
xx
xx
xx
xEM
ULoans;
To
priv.house
hold
s;Cons.
loans,
fixed
5+
yrs,outst.,bn
Euro
xx
xx
xx
xx
xx
xx
EM
ULoans;
To
priv.house
hold
s;Cons.
loans,
fixed
<1
yr,
outst.,bn
Euro
xx
xx
xx
xx
xEM
UYield
;Govern
mentbonds,
matu
rity
10
years;month
lyave.
xx
xx
xx
xx
xx
xx
xEM
UYield
;Govern
mentbonds,
matu
rity
2years;month
lyave.
xEM
UYield
;Govern
mentbonds,
matu
rity
5years;month
lyave.
xx
xx
xEM
USpre
ad;Swapsvs.
Germ
an
govt.
bonds,
mat.
2-3
y.;
Basispts;month
lyave.
xx
xx
xx
xx
EM
USpre
ad;Swapsvs.
Germ
an
govt.
bonds,
mat.
4-5
y.;
Basispts;month
lyave.
xx
xEM
USpre
ad;Swapsvs.
Germ
an
govt.
bonds,
mat.
9-1
0y.;
Basispts;month
lyave.
xEM
USpre
ad;Swapsvs.
Germ
an
govt.
bonds,
mat.
1-2
y.;
Basispts;month
lyave.
xx
EM
UExchangera
te;Euro
/US$;M
onth
lyavera
ge
xx
xx
EM
UExchangera
te;Euro
/£;M
onth
lyavera
ge
xx
xx
xEM
UExchangera
te;Euro
/100
�;M
onth
lyavera
ge
xx
xx
xx
xEM
UExchangera
te;Tra
de-w
eighte
d,nomin
al,
partnercurrencies/
Euro
;2010=100
xx
xx
EM
UIn
terb
ank
rate
,uncollate
ralized
(EURIB
OR);
3month
,offere
dx
EM
UIn
terb
ank
rate
,uncollate
ralized
(EURIB
OR);
1month
,offere
d;month
lyave.
xx
xx
EM
UIn
terb
ank
rate
,uncollate
ralized
(EURIB
OR);
12
month
,offere
d;month
lyave.
xx
EM
USwap
rate
;Euro
,1
yearvs.
6-m
onth
Lib
or;
month
lyave.
xx
EM
USwap
rate
;Euro
,2
years
vs.
6-m
onth
Lib
or;
month
lyave.
xx
xx
xx
EM
USwap
rate
;Euro
,8
years
vs.
6-m
onth
Lib
or;
month
lyave.
xEM
USwap
rate
;Euro
,9
years
vs.
6-m
onth
Lib
or;
month
lyave.
xEM
USwap
rate
;Euro
,10
years
vs.
6-m
onth
Lib
or;
month
lyave.
xEM
UCall
money
rate
,uncollate
ralized
(EONIA
);month
lyave.;
xx
xx
EM
UCitigro
up
bond
perform
ancein
dex;US$
base
d,1998.12.31=100;
xx
xx
xx
xx
xx
EM
UDJ
Euro
Sto
xx
share
pricein
dex;Euro
base
d,1991.12.31=100
xx
xx
xx
xx
xx
xEM
UDJ
Euro
Sto
xx
TM
Ish
are
perform
ancein
dex;Euro
base
d,1991.12.31=100;
xx
xx
xx
xx
EM
UDJ
Euro
Sto
xx
50
(blu
echip
)sh
are
pricesin
d.;
Euro
bs.,1991.12.31=1000
xx
xx
xx
xEM
UDJ
Euro
Sto
xx
pricein
dex;Tota
l;Euro
base
d,1991.12.31=100
xx
xx
xx
xEM
UDJ
Euro
Sto
xx
perform
ancein
dex;Tota
l;Euro
base
d,1991.12.31=100
xx
xx
xx
xx
EM
UiB
oxx
bond
perform
ancein
dex;Corp
ora
tes,
AAA,all
matu
rite
sx
xEM
UiB
oxx
bond
perform
ancein
dex;Corp
ora
tes,
BBB,all
matu
rite
sx
xx
xEM
UiB
oxx
bond
perform
ancein
dex;Corp
ora
tes,
overa
ll,all
matu
rite
sx
xEM
UiB
oxx
bond
perform
ancein
dex;Overa
ll,all
matu
rite
sx
xEM
UCitigro
up
money
mark
etperform
ancein
dex;Euro
base
d,1997.12.31=100
xEM
USto
ck
volu
mecurrently
hold
;Reta
iltrade;Balance,%
xx
xx
xx
xx
xx
xx
xEM
UCentralbank
depositra
te;M
onth
end
xx
xx
EM
U3-m
onth
Euriborfu
ture
;Neare
stexpiration;M
onth
lyavera
ge
xx
EM
UM
arg
inallendin
gfacility;Volu
meborrowed;Bn
Euro
xx
xx
xx
xx
xx
xx
xEM
UM
oney
mark
etfu
nds;
Flows,
bn
Euro
xx
xx
xEM
UM
oney
mark
etfu
nds;
12-m
onth
gro
wth
,%
xx
x
29
Tab
le5:
Selection
ofGlobal-Econom
icindicators
Hard
Soft
thre
shold
αth
resh
old
k0.01
0.05
0.1
110
20
30
40
50
60
70
80
90
100
110
120
132
World
Commodity
price(H
WW
I);Raw
mate
rials,to
tal;
US$
base
d,2010=100
xx
xx
xx
xW
orld
Commodity
price(H
WW
I);Cru
deoil;US$
base
d,2010=100
xx
xx
xx
xx
xx
xW
orld
Commodity
price(H
WW
I);Energ
ypro
ducin
gra
wmat.;US$
base
d,2010=100
xx
xx
xx
xx
xW
orld
Commodity
price(H
WW
I);Raw
mate
rials,excl.
energ
y;US$
base
d,2010=100
xx
xx
xx
xx
xx
xx
xUSA
Pro
duction;Tota
lin
dustry
excl.
constru
ction;2007=100,sa
xx
xx
xx
xx
xx
xx
xUSA
Yield
;Tre
asu
rybills,matu
rity
3month
s;M
onth
lyavera
ge
xx
xUSA
Yield
;Tre
asu
rybills,matu
rity
6month
s;M
onth
lyavera
ge
xx
xUSA
Consu
merexpecta
tions(C
onfere
nceBoard
);1985=100,sa
xx
xx
xx
xx
xx
xx
xGerm
any
Business
expecta
tions(ifo);
Manufactu
ring;Balance,%,sa
xx
xx
xx
xx
xx
xx
x
Tab
le6:
RelativeRMSFE-1stmon
th
1st
month
Hard
-thre
shold
α(k
)Soft-thre
shold
kNumberofin
dicato
rs0.01
(4)
0.05
(20)
0.1
(24)
110
20
30
40
50
60
70
80
90
100
110
120
132
Mean
0.629
0.528
0.533
0.639
0.662
0.608
0.593
0.597
0.586
0.565
0.556
0.553
0.546
0.544
0.547
0.549
0.553
Median
0.584
0.540
0.542
0.638
0.653
0.641
0.591
0.592
0.585
0.566
0.560
0.556
0.550
0.550
0.552
0.554
0.557
AIC
weighte
d0.632
0.507
0.517
0.645
0.668
0.588
0.567
0.574
0.564
0.541
0.539
0.539
0.535
0.535
0.538
0.541
0.547
R2
weighte
d0.627
0.525
0.530
0.641
0.656
0.601
0.585
0.590
0.578
0.558
0.551
0.549
0.543
0.541
0.544
0.546
0.550
Trimmed
mean
(75%)
0.604
0.469
0.500
0.731
0.683
0.564
0.542
0.545
0.544
0.521
0.533
0.534
0.535
0.539
0.544
0.550
0.557
Trimmed
mean
(50%)
0.573
0.535
0.508
0.723
0.697
0.584
0.557
0.559
0.539
0.531
0.537
0.537
0.536
0.541
0.544
0.549
0.558
Trimmed
mean
(25%)
0.593
0.555
0.517
0.643
0.652
0.595
0.576
0.576
0.558
0.542
0.539
0.537
0.536
0.539
0.542
0.548
0.556
Discounte
dM
SFE
weighte
d0.620
0.511
0.513
0.645
0.673
0.597
0.577
0.577
0.561
0.540
0.540
0.542
0.537
0.540
0.544
0.548
0.553
All
weighting
schemes
0.608
0.521
0.520
0.663
0.668
0.597
0.573
0.576
0.564
0.545
0.544
0.543
0.540
0.541
0.545
0.548
0.554
Naiveweighting
schemes
0.607
0.534
0.537
0.639
0.657
0.624
0.592
0.594
0.586
0.565
0.558
0.555
0.548
0.547
0.550
0.551
0.555
In-sample
weighting
schemes
0.630
0.516
0.523
0.643
0.662
0.594
0.576
0.582
0.571
0.550
0.545
0.544
0.539
0.538
0.541
0.543
0.549
Out-of-sa
mple
weighting
schemes
0.597
0.517
0.509
0.686
0.676
0.585
0.563
0.564
0.550
0.533
0.537
0.537
0.536
0.540
0.544
0.549
0.556
Tab
le7:
RelativeRMSFE-2n
dmon
th
2nd
month
Hard
-thre
shold
α(k
)Soft-thre
shold
kNumberofin
dicato
rs0.01
(4)
0.05
(20)
0.1
(24)
110
20
30
40
50
60
70
80
90
100
110
120
132
Mean
0.628
0.477
0.486
0.639
0.666
0.569
0.553
0.566
0.560
0.541
0.537
0.536
0.528
0.527
0.532
0.535
0.540
Median
0.578
0.492
0.500
0.638
0.647
0.603
0.560
0.570
0.569
0.555
0.548
0.548
0.538
0.539
0.543
0.544
0.549
AIC
weighte
d0.633
0.446
0.461
0.645
0.670
0.538
0.513
0.532
0.530
0.509
0.513
0.516
0.511
0.512
0.517
0.522
0.529
R2
weighte
d0.627
0.473
0.483
0.641
0.660
0.559
0.542
0.557
0.551
0.532
0.531
0.531
0.524
0.523
0.528
0.531
0.537
Trimmed
mean
(75%)
0.600
0.351
0.372
0.731
0.687
0.481
0.428
0.455
0.475
0.446
0.463
0.475
0.470
0.480
0.489
0.499
0.513
Trimmed
mean
(50%)
0.567
0.473
0.434
0.723
0.689
0.531
0.495
0.514
0.506
0.495
0.506
0.510
0.506
0.513
0.519
0.526
0.536
Trimmed
mean
(25%)
0.596
0.504
0.470
0.643
0.656
0.550
0.521
0.538
0.526
0.513
0.515
0.517
0.514
0.519
0.523
0.530
0.539
Discounte
dM
SFE
weighte
d0.620
0.424
0.426
0.645
0.672
0.520
0.483
0.499
0.499
0.468
0.478
0.486
0.485
0.491
0.497
0.504
0.514
All
weighting
schemes
0.606
0.455
0.454
0.663
0.668
0.544
0.512
0.529
0.527
0.507
0.511
0.515
0.509
0.513
0.518
0.524
0.532
Naiveweighting
schemes
0.603
0.484
0.493
0.639
0.656
0.586
0.557
0.568
0.565
0.548
0.543
0.542
0.533
0.533
0.537
0.540
0.544
In-sample
weighting
schemes
0.630
0.459
0.472
0.643
0.665
0.549
0.527
0.544
0.540
0.520
0.522
0.524
0.517
0.518
0.523
0.526
0.533
Out-of-sa
mple
weighting
schemes
0.596
0.438
0.425
0.686
0.676
0.520
0.482
0.502
0.501
0.481
0.491
0.497
0.494
0.501
0.507
0.515
0.526
30
Tab
le8:
RelativeRMSFE-3rdmon
th
3rd
month
Hard
-thre
shold
α(k
)Soft-thre
shold
kNumberofin
dicato
rs0.01
(4)
0.05
(20)
0.1
(24)
110
20
30
40
50
60
70
80
90
100
110
120
132
Mean
0.628
0.461
0.475
0.639
0.662
0.556
0.542
0.556
0.551
0.534
0.532
0.532
0.523
0.522
0.527
0.530
0.536
Median
0.577
0.475
0.490
0.638
0.639
0.579
0.543
0.560
0.556
0.545
0.542
0.543
0.532
0.534
0.538
0.540
0.545
AIC
weighte
d0.632
0.431
0.452
0.645
0.665
0.529
0.504
0.523
0.522
0.503
0.509
0.512
0.506
0.507
0.513
0.518
0.525
R2
weighte
d0.626
0.456
0.472
0.641
0.655
0.547
0.531
0.547
0.542
0.526
0.525
0.526
0.518
0.518
0.523
0.526
0.533
Trimmed
mean
(75%)
0.600
0.378
0.386
0.731
0.693
0.453
0.409
0.443
0.468
0.443
0.461
0.472
0.463
0.473
0.482
0.493
0.506
Trimmed
mean
(50%)
0.567
0.457
0.430
0.723
0.677
0.525
0.486
0.506
0.502
0.491
0.503
0.507
0.501
0.508
0.514
0.522
0.532
Trimmed
mean
(25%)
0.595
0.485
0.461
0.643
0.647
0.542
0.513
0.530
0.518
0.507
0.511
0.513
0.510
0.514
0.519
0.527
0.536
Discounte
dM
SFE
weighte
d0.619
0.420
0.426
0.645
0.670
0.495
0.461
0.479
0.483
0.456
0.469
0.478
0.477
0.483
0.489
0.497
0.507
All
weighting
schemes
0.606
0.445
0.449
0.663
0.664
0.528
0.499
0.518
0.518
0.501
0.507
0.510
0.504
0.507
0.513
0.519
0.527
Naiveweighting
schemes
0.602
0.468
0.482
0.639
0.650
0.568
0.543
0.558
0.554
0.540
0.537
0.537
0.527
0.528
0.533
0.535
0.540
In-sample
weighting
schemes
0.629
0.444
0.462
0.643
0.660
0.538
0.517
0.535
0.532
0.514
0.517
0.519
0.512
0.512
0.518
0.522
0.529
Out-of-sa
mple
weighting
schemes
0.596
0.435
0.426
0.686
0.672
0.504
0.467
0.489
0.493
0.474
0.486
0.493
0.488
0.495
0.501
0.510
0.520
31
A.3 Figures
Figure 1: Timing of forecasting exercise and availability of data
32
Figure 2: Number of indicators and their forecasting performance: Soft-thresholding: 1st month
0.300
0.400
0.500
0.600
0.700
0.800
1 10 20 30 40 50 60 70 80 90 100 110 120 132
Mean
Median
AIC weighted
R2 weighted
Trimmed mean (75%)
Trimmed mean (50%)
Trimmed mean (25%)
Discounted MSFE weighted Number of indivators
rel.
RMSF
E
Figure 3: Number of indicators and their forecasting performance: Hard-thresholding: 1st month
0.300
0.400
0.500
0.600
0.700
0.800
4 (0.01) 20 (0.05) 24 (0.1)
Mean
Median
AIC weighted
R2 weighted
Trimmed mean (75%)
Trimmed mean (50%)
Trimmed mean (25%)
Discounted MSFE weighted Number of indivators
rel.
RMSF
E
33
Figure 4: Number of indicators and their forecasting performance: Soft-thresholding: 2nd month
0.300
0.400
0.500
0.600
0.700
0.800
1 10 20 30 40 50 60 70 80 90 100 110 120 132
Mean
Median
AIC weighted
R2 weighted
Trimmed mean (75%)
Trimmed mean (50%)
Trimmed mean (25%)
Discounted MSFE weighted Number of indivators
rel.
RMSF
E
Figure 5: Number of indicators and their forecasting performance: Hard-thresholding: 2nd month
0.300
0.400
0.500
0.600
0.700
0.800
4 (0.01) 20 (0.05) 24 (0.1)
Mean
Median
AIC weighted
R2 weighted
Trimmed mean (75%)
Trimmed mean (50%)
Trimmed mean (25%)
Discounted MSFE weighted Number of indivators
rel.
RMSF
E
34
Figure 6: Number of indicators and their forecasting performance: Soft-thresholding: 3rd month
0.300
0.400
0.500
0.600
0.700
0.800
1 10 20 30 40 50 60 70 80 90 100 110 120 132
Mean
Median
AIC weighted
R2 weighted
Trimmed mean (75%)
Trimmed mean (50%)
Trimmed mean (25%)
Discounted MSFE weighted Number of indivators
rel.
RMSF
E
Figure 7: Number of indicators and their forecasting performance: Hard-thresholding: 3rd month
0.300
0.400
0.500
0.600
0.700
0.800
4 (0.01) 20 (0.05) 24 (0.1)
Mean
Median
AIC weighted
R2 weighted
Trimmed mean (75%)
Trimmed mean (50%)
Trimmed mean (25%)
Discounted MSFE weighted Number of indivators
rel.
RMSF
E
35
Figure 8: First month (soft-thresholding)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2005 2006 2007 2008 2009 2010 2011 2012 2013
tr 75 (10)
tr 75 (60)
tr 75 (full)
GDP
Solid line - GDP qoq growth rate (right axis) Bars - Forecast errors of pooled bridge models (left axis)
Figure 9: First month (hard-thresholding)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2005 2006 2007 2008 2009 2010 2011 2012 2013
tr 75 (0.01)
tr 75 (0.05)
tr 75 (full)
GDP
Solid line - GDP qoq growth rate (right axis) Bars - Forecast errors of pooled bridge models (left axis)
36
Figure 10: Second month (soft-thresholding)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2005 2006 2007 2008 2009 2010 2011 2012 2013
GDP
tr 75 (10)
tr 75 (30)
tr 75 (full)
qoq-
chan
ge in
%
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2005 2006 2007 2008 2009 2010 2011 2012 2013
tr 75 (10)
tr 75 (30)
tr 75 (full)
GDP
Solid line - GDP qoq growth rate (right axis) Bars - Forecast errors of pooled bridge models (left axis)
Figure 11: Second month (hard-thresholding)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2005 2006 2007 2008 2009 2010 2011 2012 2013
tr 75 (0.01)
tr 75 (0.05)
tr 75 (full)
GDP
Solid line - GDP qoq growth rate (right axis) Bars - Forecast errors of pooled bridge models (left axis)
37
Figure 12: Third month (soft-thresholding)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2005 2006 2007 2008 2009 2010 2011 2012 2013
tr 75 (10)
tr 75 (30)
tr 75 (full)
GDP
Solid line - GDP qoq growth rate (right axis) Bars - Forecast errors of pooled bridge models (left axis)
Figure 13: Third month (hard-thresholding)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2005 2006 2007 2008 2009 2010 2011 2012 2013
tr 75 (0.01)
tr 75 (0.05)
tr 75 (full)
GDP
Solid line - GDP qoq growth rate (right axis) Bars - Forecast errors of pooled bridge models (left axis)
38